Is there any practical application of knowing whether a concept class is PAC-learnable?
Is there any practical application of knowing whether a concept class is PAC-learnable?


If you know that a concept class is PAC-learnable (i.e. its VC dimension is finite), then there's a possibility that you can design an algorithm that can find a function (or concept) that is arbitrarily close to your target (or desired) function.

This is not really an application, but a consequence, which can lead to applications. 

However, note that asking if PAC learning is useful in practice is like asking if special relativity is useful in practice. Yes, they are useful, but in the sense that they can be used to predict the outcomes of an experiment or explain the rules in their specific context. In the case of machine learning, PAC learning can be used to explain e.g. the probably required number of data points needed to learn a concept (a target function) approximately.

See also Are PAC learning and VC dimension relevant to machine learning in practice? for more concrete "applications" of PAC-learning and the VC dimension.